The optical spectrum of the hydrated (aqueous) electron, e(aq)(-), is the primary observable by means of which this species is detected, monitored, and studied. In theoretical calculations, this spectrum has most often been simulated using one-electron models. Here, we present ab initio simulations of that spectrum in both bulk water and, for the first time, at the water/vapor interface, using density functional theory and its time-dependent variant. Our results indicate that this approach provides a reliable description, and quantitative agreement with the experimental spectrum for the bulk species is obtained using a "tuned" long-range corrected functional. The spectrum of the interfacial electron is found to be very similar to the bulk spectrum.